In the current manuscript we are mainly concerned with a novel
gravitational theory, closely related to \(f(\mathcal {G},\mathrm {T})\)  gravity that enables the term \(\mathbf {L}_{GR}\)  to
depend on some analytic function of the scalar \(\mathbf {T}^{2}\)  is
characterized by \(f(\mathcal {G}, \mathbf {T}^{2})\) , where
\(\mathbf {T}^{2}\equiv T_{\alpha \beta }T^{\alpha \beta }\) . The
underlying principal for using such material stresses stems from the
rational as illustrated by Katirci and Kavuk [1]}.
Such type of modifications of \(\mathrm {GR}\)  comprises additional
contributions from the material stresses to the \(\mathrm {GR}\) 
equations of motion. It is reasonable to consider that the
correction term \(\mathbf {T}^{2}\)  will be significant only in regions
of relatively high energy for example within black holes or the
early-time cosmos. The presence of regular bounce and maximum energy
density in the early cosmos in this gravity theory shows that this
can address the Big Bang singularity with both non-quantum and
classical methods. It is worth mentioning that \(\mathrm {EMSG}\) 
resolve the issue of space-time singularity without changing the
cosmological evolution [2]}.
